The spin-forbidden transition in iron(IV)-oxo catalysts relevant to two-state reactivity

Quintet oxoiron(IV) intermediates are often invoked in nonheme iron enzymes capable of performing selective oxidation, while most well-characterized synthetic model oxoiron(IV) complexes have a triplet ground state. These differing spin states lead to the proposal of a two-state reactivity model, where the complexes cross from the triplet to an excited quintet state. However, the energy of this quintet state has never been measured experimentally. Here, magnetic circular dichroism is used to assign the singlet and triplet excited states in a series of triplet oxoiron(IV) complexes. These transition energies are used to determine the energies of the quintet state via constrained fitting of 2p3d resonant inelastic x-ray scattering. This allowed for a direct correlation between the quintet energies and substrate C─H oxidation rates.

The MCD spectra for all three complexes (Figures S2 and S3) show a complex temperature dependence below 16000 cm -1 .At lower temperatures the feature has nearly entirely positive MCD intensity, but as the temperature increases the low-energy portion of the spectra loses intensity until by 40K there is negative MCD intensity.The higher-energy portion of this region maintains a positive MCD, which increases with increasing temperature until ~20K then decreases in all complexes at higher temperatures.All three complexes show a resolved vibronic structure similar to what has been seen in previous MCD studies on iron(IV)-oxo complexes.A similar Franck-Condon analysis is applied to these bands in the section below.At higher energies for N2Q are weak, separated positive features followed by an intense negative and then positive derivative shape.For DMM and N4py the positive intensity is broader and relatively more intense, and there is only the strong negative feature at ~26000 cm -1 .
For interpretation of the MCD spectra, Gaussian deconvolution was used with minimal bands of 10 for N2Q, and 9 for DMM and N4py. Figure S4 shows the results of these fits at 2.5K and 40K for each of the three complexes.The energies and variable-temperature dependence (Figure S5) of the bands can be used along with NEVPT2 calculations to assign the states for each transition.For ligandfield excitations, NEVPT2 can get quantitatively accurate results (see Table S4).For charge-transfer (CT) transitions, or ligand-field transitions with considerable CT character, NEVPT2 can fail to accurately predict these energies if the ligand-based orbitals are outside of the active space.
Bands 4 and 5 are used to fit the vibronic structure described below, and together the two Cterms give a positive pseudo-A term (the higher energy of the two C-terms is positive).Despite the substantial overlap of the vibronic structure with additional bands, for DMM and N4py below 11000 cm -1 there is an isolated negative band at all temperatures, giving confidence to sign of the pseudo-A term by having lower-energy negative features.The temperature dependence of the bands give a largely xy dominated polarization, and taking this into combination with the sign of the pseudo-A term and vibronic progression (based on previous iron(IV)-oxo studies) would assign these bands as the 3 A2 ® 4-3 E(1b2(dxy) ® 2e(dxz/yz)) transitions.The NEVPT2 energies for the states support this assignment, as these are calculated to be the lowest energy spin-allowed transitions in all three complexes.Bands 6, 7, 8 and 9 contain substantial overlap of intensity and lead to the complex temperature dependence of the spectra.Bands 6 and 8 are largely overlapping, which could lead to some uncertainty in the exact intensity of each band, however due to the eventual negative intensity at higher temperatures, both a positive and negative band are needed to accurately describe the spectra.Based on the agreement with calculated transitions, as well as the xy-polarization determined from temperature dependence, bands 6 and 7 are assigned as the two C-terms describing the positive pseudo-A term of the 3 A2 ® 2-3 E(2e(dxz/yz) ® 2b1(dx2-y2)) (56).With the three complexes present in the study, the absolute values can also be used along with the relative values between complexes for comparison of the experimental and calculated values.For the 3 A2 ® 2-3 E transition, there is both an experimental and calculated shift of ~500 cm -1 N2Q to lower energy compared to N4py/DMM.
The temperature dependence of band 8 indicates it is a z-polarized transition.This has been previously assigned to the 3 A2 ® 2-3 A2 (1b2(dxy) ® 2b1(dx2-y2)) or 3 A2 ® 3-3 A2 (1b2(dxy) ® 2a1(dz2)) transitions in similar complexes, and calculated energies would support the assignment to the 3 A2 ® 2-3 A2 (1b2(dxy) ® 2b1(dx2-y2)) transition.It has been predicted that the two-electron A2 transition gains intensity due to the actual lower symmetry of the complex, Cs, which allows for mixing with nearby excited states.For the experimental values the transition in N2Q is ~2300 cm -1 lower than N4py and DMM, and the calculated values have N2Q 1400 cm -1 lower in energy, predicting a smaller difference but still larger than that seen for the 3 A2 ® 2-3 E transition.
The temperature dependence of band 9 is nearly purely xy-polarized.This temperature dependence supports the assignment as the 3 A2 ® 3-3 E (2e(dxz/yx) ® 2a1(dz2)) transition.It would be expected for the transition to exhibit a pseudo-A term from the two C-term components, but these transitions are calculated to mix heavily with charge-transfer transitions, and intense CT transitions can distort the band shapes leading to a standard C-term feature (56).The 3 A2 ® 3-3 E transition for N2Q is determined to be 3000 cm -1 lower in energy than for N4py and DMM.For N4py and DMM, the two states are calculated to be nearly degenerate while for N2Q the two states are predicted to be approximately 2000 cm -1 apart.Overall, the splitting between the states is 4100 cm -1 between the lowest energy N2Q 3-3 E state and N4py/DMM, and 1800 cm -1 between the higher energy N2Q 3-3 E state and N4py/DMM.This puts the average energy difference between the complexes at 3000 cm -1 , in excellent agreement with the experimental splitting.
For Band 10, the temperature dependence gives mixed polarization with considerable zpolarized character.This mixture of polarization leads to an assignment of the spin-allowed 3 A2 term, 3-3 A2(1b2(dxy) ® 2a1(dz2)).The 2-electron 3-3 A2 term is calculated to have significant (>20%) LMCT mixing.For CASSCF/NEVPT2 calculations, there is an overestimation of excitation energies of CT excited states, leading to a larger deviation in the calculated energies vs experimental energies for these heavily mixed states.The values of the 3-3 A2 deviate significantly from the experimental values, ~9000 cm -1 higher in energy.This has been seen consistently for the CASSCF/NEVPT2 calculations of this specific state.(27) The trend in relative energies, however, agrees very well with what is measured experimentally.N2Q is calculated to be 2000 cm -1 lower in energy than N4py/DMM, while experimentally it was determined to have a 3-3 A2 state 2300 cm -1 lower in energy.
Finally bands 11, 12, and for N2Q band 13 reside at the upper limit of the energy range.These bands experimentally show small variation between the complexes, with bands 11 and 12 both ~400 cm -1 lower in energy for N2Q than N4py/DMM.This lack of ligand field effect could be indicative of LMCT states.In the CASSCF/NEVPT2 calculations the LMCT dominated states begin to arise above 30000 cm -1 .For p ® p* transitions, it would be expected that excitation from a highly covalent bonding orbital into the corresponding antibonding orbital would lead to an intense transition with significant MCD intensity.This would indicate band 12 (and 13) to arise from p ® p* transitions.Additionally, the excitation from the 1e to 2e would lead to the pseudo-A term as seen in the MCD.Finally, when comparing the p ® p* transitions between complexes, there is only a small shift in the calculated values of ~500 cm -1 , in agreement with the experimental shifts of band 12.For band 11, the small shift still suggests an LMCT, but the weak intensity would indicate excitation from less covalent, or non-oxygen ligand-based orbital.Including these orbitals into the active space would make the calculations too costly, and as such the exact assignment of band 11 cannot be obtained at this time.

MCD of Glass and Mull sample
The glass and mull powder MCD spectra are overlaid in Figure S7.The singlet transitions are shown to be insensitive to the sample environment.Vibronic Structure.Bands 1 and 2 have been previously assigned in similar iron(IV)-oxo complexes as the 3 A2 ® 3 E(1b2(dxy) ® 2e(dxz/yz)) transition, so that the spacing between the peaks arise from the excited state Fe-O stretching frequency (ℎ !" ) (26)(27)(28).Since this is an excitation into the Fe-O p* orbitals, this elongates the bond, reducing the force constant and lowering the vibrational energy of the stretching mode relative to the ground state.The band shape from the intensity of each band is described by a Poisson distribution: Where  #$# and  #$% represent the vibronic transitions from the 0 to 0, and the respective 0 to n vibrational energy levels,  &' is the Huang-Rhys factor described by: Where  !" is the excited state force constant, Dr is the distortion in the excited state structure which for this transition represents an elongation in the Fe-O bond, and ℎ !" is the excited state vibrational energy.The Huang-Rhys factor represents the change in the potential energy surface due to geometric distortions of the excited state structure.For N4py, ℎ !" was reported to be ~500 cm -1 and  &' was reported to be ~4.5 (26).Fits here give values of ℎ !" = 530 +/-18 cm -1 and  &' a value of 4.48.For DMM, the shape and intensity of the vibronic progression is similar to that of N4py, and values of ℎ !" = 524 +/-20 cm -1 and  &' = 4.55 were derived from the fits.N2Q shows a different band structure with a significantly populated 0-0 band, and with greater individual band intensities overall.The values derived from the fits of N2Q are ℎ !" = 572 +/-28 cm -1 and  &' = 2.81.

Iron(II) RIXS
The RIXS cuts for the iron(II) complexes of N2Q-2+, DMM-2+, and N4py-2+ are shown in Figure S9.The high-spin (HS) N2Q-2+ has a well separated peak at 1.2 eV at all incident energies with a shoulder that grows in at higher incident energies.This peak corresponds to the spin-allowed dd transitions (Figure S8 and FigureS9).At higher energy transfer there are overlapping features around 2.6 eV that grow in relative intensity with increasing incident energy, and with 710.6 eV incident energy a third feature around 4 eV energy transfer.The low-spin (LS) DMM-2+ and N4py-2+ are very similar, with significantly more overlapping features than the HS iron(II) complex.In the 708.1 and 708.6 eV cuts, there are peaks at 1.5 and 2.0 eV that lose definition in the higher incident energy 710.6 eV cut.
The HS iron(II) complex, N2Q-2+, is calculated to have a nearly degenerate S = 2 ground state, and a low-lying S = 2 state 0.124 eV above the ground state.The next lowest lying states are S = 2 at 1.3 eV, with minimal splitting implying nearly degenerate eg orbitals.At higher energies there are two sets of densely packed spin-forbidden transitions, which align with the shoulder at 1.5 eV that gains intensity at higher incident energy, and the second, higher energy peak at 2.6 eV.
The LS iron(II) complexes, N4py-2+ and DMM-2+, are both calculated to have no states lower in energy than approximately 1.5 eV.There are a multitude of ΔS = +1/+2 transitions between 1.5 and 2.5 eV, where at 2.5 eV the first ΔS = 0 transitions are calculated to be.The ΔS = 1 transitions line up nicely with the features at approximately 1.5 and 2.0 eV, and the first ΔS = 0 transition is in agreement with the large peak at approximately 2.3 eV in the 708.1 and 710.6 eV cuts.The largest peak shifts to 2.5 eV in the 708.6 eV cut, though the CAS calculations are underestimating this transition by ~0.1 eV.

Iron(IV)-oxo RIXS
The 2p3d RIXS for the three complexes are shown in Figure S10.The cut with a 706.6 eV incident energy displays two separated features for all three complexes, with the sharper, more intense peak at approximately at 1.3 eV and the broader, weaker feature at approximately 2.6 eV.Increasing the incident energy to 708.1 eV causes a loss of definition in the complexes, but in N4py and DMM a feature grows in at around 2.2 eV, while in N2Q the intensity peaks around 1.5 eV.With an incident energy of 708.6 eV, N4py remains largely unchanged while DMM and N2Q becomes more welldefined.Further increasing the incident energy to 710.6 eV causes significant changes in the RIXS, with intensity below 1 eV becoming apparent in all complexes, as well as a shoulder around 1.4 eV and a peak around 2.3 eV.For the lower energy transfer feature, in N4py is appears as a small shoulder around 1 eV, the DMM shows a larger separation and is around 0.85 eV, and the N2Q appears as a distinct peak at approximately 0.7 eV.Fits of the data are performed both with energies held (Figure S11) at the values from the MCD fits, as well as using freely floating peak energies (Figure S12).In the 0.4 to 1.0 eV range, both fits contain a constant Gaussian function at approximately 0.66 eV, which in the MCD-derived fits corresponds to the lowest triplet to singlet transition.From the MCD fitting, the N2Q, DMM and N4py have a function at 0.45 eV, 0.86 and 0.94 eV, respectively.From the freely floating peak fitting, the features are at 0.47, 0.85, and 0.95 for N2Q, DMM, and N4py, respectively.As the triplet to singlet transitions remain at nearly constant energy for all three complexes, the change in shape of the 708.6 and 710.6 eV cut requires a Gaussian function that shifts significantly in energy between complexes.This is consistent in both methods of fitting the RIXS cuts.In Figure S13, the fits are shown excluding the 5 A1 peak, and the reduced c 2 are shown in table S7.

Mössbauer for iron(IV)-oxo complexes
The 2K, zero-field Mössbauer spectra are shown in figure S16 for the three oxo complexes.As the solid powders could be generated in large quantities, unenriched samples were used for these measurements.The fitted parameters are shown in Table S8.As only one quadrupole doublet was necessary in simulation for the fits, the samples are composed purely of the S=1 iron(IV)-oxo complexes within the limit of detection of the method.S9.

Figure S3 .
Figure S3.VT 10T MCD of the low-energy NIR feature for N2Q, DMM, and N4py

Figure S5 .
Figure S5.Spin Hamiltonian simulations.Spin Hamiltonian simulations for the MCD data and fits in the UV/Vis region between 2.5 and 40 K with 10T applied field for N2Q, DMM, and N4py.Peak numbers are indicated on the right.

Figure S7 .
Figure S7.Comparion of MCD at 10T and 40K for N2Q of glass and mull sample.MCD at 10T and 40K for N2Q of a frozen solution glass sample and a mull sample over the UV/Vis range (left) and NIR range (right).The low-energy features in the NIR region remain unchanged in energy.

Figure S8 .
Figure S8.RIXS cuts for iron(II) complexes.RIXS cuts for the iron(II) complexes of N2Q, DMM, and N4py out to 10 eV energy transfer.Incident energies are shown in figure for each cut.

Figure S12 .
Figure S12.RIXS cuts for iron(IV)-oxo complexes with floated fits.RIXS cuts for the iron(IV)oxo complexes with fitted functions with energies freely floating.Below 1 eV, all three complexes have a fitted function at ~0.66 eV corresponding to the singlet transition, and a moving function from 0.47 (N2Q), 0.85 (DMM), and 0.95 (N4py) corresponding to the 5 A1 feature.

Figure S13 .
Figure S13.RIXS cuts for the iron(IV)-oxo complexes with MCD held intensities without the floated peak for the 5 A1 state

Table S1 .
CASSCF configurations and weights for state specific triplet and quintet states and the three state averaged singlet states.Doubleshell orbitals are excluded from table and all are unoccupied.

Table S3 .
Experimental and CASSCF/NEVPT2 Triplet to Singlet Energy Differences (eV) MCD Band Assignment for Spin-Allowed Transitions.

Table S4 .
MCD Peaks and polarizations

Table S5 .
Parameters derived from fits of the vibronic structure.

Table S6 .
(21)ced c 2 for the fits with and without the 5 A1 function for the RIXS cuts at 708.6 and 710.6 eV.Data from reference 19 b Data from this work c Data from reference(21) Figure S14.ORTEP of DMM.ORTEP plots of DMM with thermal ellipsoids set at 50% probability.Hydrogens and counterions are removed for clarity.Table S7.Selected geometric parameters for the iron(IV)-oxo complexes a N4py b DMM c N2Q

Table S8 .
Crystallographic data of DMM.